It is hardly surprising, given that they are in coalition with the Liberal Democrats, that the Conservative party is in something of a conflicted mood as it meets in Manchester this week. The Tories have much to feel confident about, nevertheless. They are in government, albeit not on the majoritarian terms they would prefer. Their poll ratings are resilient – no significant loss of support since the general election. David Cameron remains clearly the most popular of the three main party leaders. Most important of all, the government remains more trusted than Labour on the economy, even in increasingly difficult times, against which the TUC rallied in Manchester yesterday. With Labour failing to make big inroads, it is not surprising that most Tories feel cautiously satisfied.

Yet wiser heads in the party are rightly concerned with what this record masks. Things may be about to get a lot worse before they, hopefully, get better. With inflation and unemployment rising, negligible growth and global markets febrile, even harder times are looming. Increasingly, the government is on the defensive. This weekend, there has been a flurry of publicity for the weakening of Tory support among women voters and the skilled working class generally. As the economy stagnates, the coalition's credibility weakens. Popularity has to be fought for again, especially among less well-off voters. Tensions are rising within the party about the government's direction.

Power enables the Tories to do what any governing party can do and no opposition party can emulate at such moments. As the conference gathered at the weekend, ministers promised goodies: from Philip Hammond's review of the speed limit, designed to appeal to the party's Clarkson wing, through Eric Pickles's promise of weekly bin collections, to George Osborne's pledge to raise the threshold for bringing unfair dismissal claims, a key demand from the party's core funders. Yesterday Mr Cameron focused on the housing market, promising a boost both to the right to buy and to housebuilding in an attempt to show he has a growth agenda. Mr Osborne will have new growth announcements when he speaks today.

The economy clearly holds the key to whether the coalition parties will prosper or falter. Yet the Conservatives face other big challenges this week. Pressure to appease the unreconciled Tory right is noisy. Now that the first flush of government is over, the right focuses, as ever, on Europe and the abolition of the Human Rights Act (to which Theresa May pandered yesterday). It increasingly flirts with the Boris Johnson for Leader bandwagon encouraged in parts of the media. It pretends that the coalition does not exist, that the Tories are more popular than they are and deludes itself that a leader other than Mr Cameron would carry the party to an overall majority.

Luckily for the Tories, this view is not shared across this still very deferential party. Nevertheless, one of the most important issues to watch this week is whether Mr Cameron and the pragmatists manage to push back against the right. Their strategy in Manchester is to reassert the modernising spirit and agenda Mr Cameron promoted in his early days as leader and which remains his party's greatest electoral asset. The prime minister himself is key to this. But the same attempt at renewing the modernising appeal runs through the party's new pamphlet on compassionate conservatism. It could be seen in Andrew Mitchell's robust reassertion of the overseas aid agenda yesterday, and in William Hague's significant pragmatism towards the EU in his Observer interview. Later, in the hall, Mr Hague went out of his way to defend the coalition and to praise Nick Clegg, a brave thing to do. This is not a crisis week for the Conservatives, but the fact that so much depends on showcasing Mr Cameron's leadership is a reminder both of the party's strength and of its continuing wider weakness.